On Jacobi fields

Details On Jacobi fields On Jacobi fields

Feb 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977gregr...8...95n&link_type=abstract

General Relativity and Gravitation, vol. 8, Feb. 1977, p. 95-102.

Mathematics

1

Gravitation Theory, Jacobi Integral, Relativity, Riemann Manifold, Curves (Geometry), Geodesic Lines, Gravitational Effects, Metric Space, Singularity (Mathematics), Space-Time Functions, Tensor Analysis

Scientific paper

Curves on a Riemannian manifold are defined as integrals of generalized Jacobi fields. It is shown that the force term that deviates the trajectory from geodesic motion can be constructed as a functional of the metric tensor. These curves can be interpreted as particles (observers) coupled nonminimally with gravitation and which can provide a class of residual observers for the inevitable singularity.

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